Category Theory: Lectures |
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A₂ Abel abelian category abelian group adjoint functors adjunction algebra axioms B₁ B₂ base point bifunctor category theory category with zero cokernel cokernel of f composite consider contravariant functor coproduct DEFINITION Denote dual element epimorphism exact functor example exists F P₁ F P₂ F preserves f₁ f₂ finite free group function functor F fundamental group given group structure H-objects homomorphism homotopy theory identity implies inverse isomorphism kernel language of categories left adjoint left exact lemma loop mathematics module monic morphism f natural equivalence natural transformation notation preserves epics PROOF PROPOSITION prove pull-back push-out right exact sequence short exact sequence singleton space Suppose F surjective THEOREM topological group triple underlying functors unique X₂ Z₂ zero morphism zero object Аг